Most Libby's are named after a woman named Libe ( love or beloved ) pronounced "LEE-beh. sometimes shown as Liba . It is also possible that it could be Leah/Leye , but that is less likely . 

Shirley is most often Sarah i.e Sore/Sure/Surke/Sorl/Surl etc. , but it could also be Sheyndl (SHEYN-dl ) from sheyn ( pretty or beautiful ) which also yields Sheyne /Shana/Shane/Shena  in English . Shifre ( SHIF-reh ) is also  possible.

As others have said , there are many possibilities,  but the most common are Libe and Sore/Sure etc. 
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Henry H. Carrey